No definite viewpoint for the accelerating traveler?

[Dale]

On the same page that you reference, one sees the following:

"Schemes for locating points in a given space by means of numerical quantities specified with respect to some frame of reference. These quantities are the coordinates of a point. To each set of coordinates there corresponds just one point in any coordinate system, but there are useful coordinate systems in which to a given point there may correspond more than one set of coordinates"

Emphasis mine.

These are not valid coordinate charts in GR. Other disciplines may make use of such coordinates, but not GR.

 

[jbriggs444]

You are being quite rude with your later posts to PAllen for no reason at all as he is correcting a very absurd statement you are making. A coordinate map is an n - tuple of coordinate functions on an open subset of the manifold representing space - time. You are claiming the coordinate map can take a point in this region and map it to two different coordinates (the events that characterize the space - time aspect of the manifold for a given family of observers). This is not even a problem of physics, you are going against the very definition of a function which is a basic set theoretical object.

Rather than continue this distraction, I will bow out, acknkowledging that I am at the very least using standard terminology incorrectly for purposes of this context.

 

[WannabeNewton]

A function need not be injective mate but it cannot map a value in the domain to two values in the range which is what you are doing by assigning two different events to the same point on the manifold for a single observer.

 

[Alain2.7183]

I've been looking at a lot of the posts that Mentz recommended to me in another thread:

What is CADO?

See this topic

https://www.physicsforums.com/showthread.php?t=490163

I also did a forum search on "CADO", and found some more recent posts, including this one:

https://www.physicsforums.com/showpost.php?p=4041919&postcount=287

That post showed what someone who is going around and around in a circle, at constant speed, would say is the current age of some inertial person who is located some distance away from the circle. That post was interesting to me, because it is very similar to an example that I saw in a NOVA program called "the fabric of the cosmos". There, Brian Greene gave an example of someone on a planet in an extremely distant galaxy, who is riding a bicycle around and around in a small circle, and who says that for each of his loops, the time here on Earth is swinging back and forth over centuries! Brian Greene got that result by using the spatial three-dimensional "simultaneous time slices" of the sequence of inertial frames that are momentarily co-moving with the bicycle rider. Brian also has essentially the same example in his book that has the same title as the NOVA show.

As far as I can recall, in both the TV show and in his book, Brian didn't seem to be presenting his method as "just one of several different possible answers" to the question of "What is the current age of the inertial person, according to the accelerating person?". My impression was that he seemed to present it as THE answer.

On my CADO forum search, I also found this link,

https://sites.google.com/site/cadoequation/cado-reference-frame

that seems to give a pretty good summary of all the CADO stuff. The CADO equation explained in there gives the same result as Brian Greene's "momentarily co-moving inertial frame" method, but it's quicker and easier.

 

[PAllen]

As far as I can recall, in both the TV show and in his book, Brian didn't seem to be presenting his method as "just one of several different possible answers" to the question of "What is the current age of the inertial person, according to the accelerating person?". My impression was that he seemed to present it as THE answer.

This is Brian Greene in a pop-sci setting. Further, you are probably reading more into than Greene intended - I doubt he explicitly said this is the one valid way to look at things. A generic issue with pop-sci is that you select one simple, WOW point of view to describe about a more complex, multi-faceted situation. Also, if you want to argue by reference to authority, I could respond my noting that never in Einstein's life did he use such lines of simultaneity in either SR or GR.

 

[Dale]

Brian didn't seem to be presenting his method as "just one of several different possible answers" to the question of "What is the current age of the inertial person, according to the accelerating person?". My impression was that he seemed to present it as THE answer.

THE answer to what question?

If the question is "how can you do physics in a non-inertial frame" then it is not even an answer let alone THE answer. If the question is "what is the naive non-inertial simultaneity convention which most novices tend to adopt and which is useless for any actual physics" then I would agree that it is probably THE answer.